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The Dimension of Cohomological Support Varieties

Connections Workshop: Commutative Algebra January 18, 2024 - January 19, 2024

January 18, 2024 (11:00 AM PST - 12:00 PM PST)
Speaker(s): Eloísa Grifo (University of Nebraska)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC

The Dimension of Cohomological Support Varieties


Given a complex of R-modules M, one can construct a variety that contains homological information about M called the cohomological support variety V_R(M). These have various homological applications – for example, Pollitz showed they can be used to characterize when R is a complete intersection. In this talk, we will discuss the following realizability question: given an appropriately chosen variety V, when can V be realized as V_R(M) for some M? To study this question, we give bounds on the dimension of such varieties. This is joint work with Ben Briggs and Josh Pollitz.

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The Dimension of Cohomological Support Varieties

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